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<div id="Sx1" class="ltx_section">
<h1 class="ltx_title ltx_title_section">Lowered Gaussian filter</h1>

<div id="Sx1.p1" class="ltx_para">
<p class="ltx_p">This filter was reported to perform well in the DAOPHOT <cite class="ltx_cite">[<a href="#bib.bib34" title="DAOPHOT - A computer program for crowded-field stellar photometry" class="ltx_ref">2</a>]</cite>
and DAOSTORM <cite class="ltx_cite">[<a href="#bib.bib12" title="DAOSTORM: an algorithm for high- density super-resolution microscopy" class="ltx_ref">1</a>]</cite> algorithms. The <a href="Convolution.html" title="" class="ltx_ref">convolution kernel</a>
is based on the <a href="GaussianFilterUI.html" title="" class="ltx_ref">Gaussian kernel</a> which
has been lowered to have the sum of all its entries equal to zero,</p>
<table id="Sx1.Ex1" class="ltx_equation">

<tr class="ltx_equation ltx_align_baseline">
<td class="ltx_eqn_pad"></td>
<td class="ltx_align_center"><img id="Sx1.Ex1.m1" class="ltx_Math" style="vertical-align:-6px" src="mi/mi68.png" width="265" height="21" alt="K_{\mathrm{LG}}\left(x,y\mid\sigma\right)=K_{\mathrm{G}}\left(x,y\mid\sigma%
\right)-b\,,"></td>
<td class="ltx_eqn_pad"></td>
</tr>
</table>
<p class="ltx_p">where <img id="Sx1.p1.m1" class="ltx_Math" style="vertical-align:-2px" src="mi/mi70.png" width="12" height="16" alt="b"> is the mean value of all of the elements in <img id="Sx1.p1.m2" class="ltx_Math" style="vertical-align:-5px" src="mi/mi62.png" width="31" height="18" alt="K_{\mathrm{G}}">.
The standard deviation <img id="Sx1.p1.m3" class="ltx_Math" style="vertical-align:-2px" src="mi/mi63.png" width="15" height="12" alt="\sigma"> is a user-specified parameter.</p>
</div>
<div id="Sx1.p2" class="ltx_para">
<p class="ltx_p">Although the kernel <img id="Sx1.p2.m1" class="ltx_Math" style="vertical-align:-5px" src="mi/mi69.png" width="40" height="18" alt="K_{\mathrm{LG}}"> is not separable, the filtered
image can be obtained by subtracting two images filtered with two
separable kernels (see <a href="Convolution.html" title="" class="ltx_ref">convolution with separable kernels</a>),</p>
<table id="Sx1.Ex2" class="ltx_equation">

<tr class="ltx_equation ltx_align_baseline">
<td class="ltx_eqn_pad"></td>
<td class="ltx_align_center"><img id="Sx1.Ex2.m1" class="ltx_Math" style="vertical-align:-5px" src="mi/mi67.png" width="268" height="18" alt="F=I*K_{\mathrm{LG}}=I*K_{\mathrm{G}}-I*K_{\mathrm{AV}}\,."></td>
<td class="ltx_eqn_pad"></td>
</tr>
</table>
<p class="ltx_p">The lowered Gaussian is a band-pass filter. The sizes of both <img id="Sx1.p2.m2" class="ltx_Math" style="vertical-align:-5px" src="mi/mi62.png" width="31" height="18" alt="K_{\mathrm{G}}">
and <img id="Sx1.p2.m3" class="ltx_Math" style="vertical-align:-5px" src="mi/mi2.png" width="39" height="18" alt="K_{\mathrm{AV}}"> kernels are computed as <img id="Sx1.p2.m4" class="ltx_Math" style="vertical-align:-6px" src="mi/mi66.png" width="110" height="21" alt="l=1+2\left\lceil 3\sigma\right\rceil">.</p>
</div>
<div id="Sx1.SSx1" class="ltx_subsection">
<h2 class="ltx_title ltx_title_subsection">Threshold for approximate localization of molecules</h2>

<div id="Sx1.SSx1.p1" class="ltx_para">
<p class="ltx_p">The <a href="../../detectors/Threshold.html" title="" class="ltx_ref">threshold</a> value can be
specified by users as an expression combining mathematical functions
and operators with variables based on the current raw or filtered
image. Variables provided by this filter are:</p>
</div>
<div id="Sx1.SSx1.p2" class="ltx_para">
<table class="ltx_tabular ltx_align_middle">
<tbody class="ltx_tbody">
<tr class="ltx_tr">
<td class="ltx_td ltx_align_left"><span class="ltx_text ltx_font_typewriter">LowGauss.I</span></td>
<td class="ltx_td ltx_align_left">current raw input image</td>
</tr>
<tr class="ltx_tr">
<td class="ltx_td ltx_align_left"><span class="ltx_text ltx_font_typewriter">LowGauss.F</span></td>
<td class="ltx_td ltx_align_left">corresponding filtered image</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="Sx1.SSx2" class="ltx_subsection">
<h2 class="ltx_title ltx_title_subsection">See also</h2>

<div id="Sx1.SSx2.p1" class="ltx_para">
<ul id="I1" class="ltx_itemize">
<li id="I1.i1" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_itemize">•</span> 
<div id="I1.i1.p1" class="ltx_para">
<p class="ltx_p"><a href="Filters.html" title="" class="ltx_ref">Image filtering and feature enhancement</a></p>
</div>
</li>
<li id="I1.i2" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_itemize">•</span> 
<div id="I1.i2.p1" class="ltx_para">
<p class="ltx_p"><a href="../../detectors/Detectors.html" title="" class="ltx_ref">Finding approximate positions of molecules</a></p>
</div>
</li>
</ul>
</div>
</div>
</div>
<div id="bib" class="ltx_bibliography">
<h1 class="ltx_title ltx_title_bibliography">References</h1>

<ul id="L1" class="ltx_biblist">
<li id="bib.bib12" class="ltx_bibitem ltx_bib_article">
<span class="ltx_bibtag ltx_bib_key ltx_role_refnum">[1]</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_author">S. J. Holden, S. Uphoff and A. N. Kapanidis</span><span class="ltx_text ltx_bib_year">(2011)</span>
</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_title">DAOSTORM: an algorithm for high- density super-resolution microscopy</span>,
</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_journal">Nature Methods</span> <span class="ltx_text ltx_bib_volume">8</span> (<span class="ltx_text ltx_bib_number">4</span>), <span class="ltx_text ltx_bib_pages"> pp. 279–80</span>.
</span>
<span class="ltx_bibblock">External Links: <span class="ltx_text ltx_bib_links"><a href="http://dx.doi.org/10.1038/nmeth0411-279" title="" class="ltx_ref doi ltx_bib_external">Document</a></span>.
</span>
<span class="ltx_bibblock ltx_bib_cited">Cited by: <a href="#Sx1.p1" title="Lowered Gaussian filter" class="ltx_ref"><span class="ltx_text ltx_ref_title">Lowered Gaussian filter</span></a>.
</span>
</li>
<li id="bib.bib34" class="ltx_bibitem ltx_bib_article">
<span class="ltx_bibtag ltx_bib_key ltx_role_refnum">[2]</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_author">P. B. Stetson</span><span class="ltx_text ltx_bib_year">(1987)</span>
</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_title">DAOPHOT - A computer program for crowded-field stellar photometry</span>,
</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_journal">Publications of the Astronomical Society of the Pacific</span> <span class="ltx_text ltx_bib_volume">99</span>, <span class="ltx_text ltx_bib_pages"> pp. 191</span>.
</span>
<span class="ltx_bibblock">External Links: <span class="ltx_text ltx_bib_links"><a href="http://dx.doi.org/10.1086/131977" title="" class="ltx_ref doi ltx_bib_external">Document</a></span>.
</span>
<span class="ltx_bibblock ltx_bib_cited">Cited by: <a href="#Sx1.p1" title="Lowered Gaussian filter" class="ltx_ref"><span class="ltx_text ltx_ref_title">Lowered Gaussian filter</span></a>.
</span>
</li>
</ul>
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